You exile cards from your graveyard at the same time you pay the spell’s cost. Exiling a card this way is simply another way to pay that cost.

11/24/2014

Delve doesn’t change a spell’s mana cost or converted mana cost. For example, the converted mana cost of Tasigur’s Cruelty (with mana cost ) is 6 even if you exile three cards to cast it.

11/24/2014

You can’t exile cards to pay for the colored mana requirements of a spell with delve.

11/24/2014

You can’t exile more cards than the generic mana requirement of a spell with delve. For example, you can’t exile more than five cards from your graveyard to cast Tasigur’s Cruelty.

11/24/2014

Because delve isn’t an alternative cost, it can be used in conjunction with alternative costs.

12/7/2018

Tasigur’s last ability doesn’t target any card or player. You choose an opponent as the ability resolves and that player chooses a nonland card after you put the top two cards of your library into your graveyard.

12/7/2018

The chosen opponent can choose any nonland card in your graveyard, not just one of the cards that was just put there.